Automatic segmentation of the cerebral cortex from magnetic resonance brain images is a valuable tool for neuroscience research. Due to the presence of noise, intensity non-uniformity, partial volume effects, the limited resolution of MRI and the highly convoluted shape of the cerebral cortex, segmenting the brain in a robust, accurate and topologically correct way still poses a challenge. In this paper we describe a topologically correct Expectation Maximisation based Maximum a Posteriori segmentation algorithm formulated within the Khalimsky cubic complex framework, where both the solution of the EM algorithm and the information derived from a geodesic distance function are used to locally modify the weighting of a Markov Random Field and drive the topology correction operations. Experiments performed on 20 Brainweb datasets show that the proposed method obtains a topologically correct segmentation without significant loss in accuracy when compared to two well established techniques.